Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_yellow 6 3.485128
beta0_yellow 6 2.180652
beta1_yellow 7 2.079704
sd_comp 1 1.338571
beta2_yellow 7 1.246299
beta2_pelagic 1 1.224968
beta4_pelagic 1 1.205183
parameter n badRhat_avg
beta1_pH 6 1.197200
mu_beta0_yellow 2 1.196382
beta1_pelagic 3 1.158019
tau_beta0_yellow 2 1.145256
beta0_pelagic 2 1.134593
beta2_pH 1 1.130265
Table 2. Summary of unconverged parameters by area
afognak BSAI CSEO eastside NG NSEI NSEO PWSI PWSO SOKO2SAP SSEO WKMA
beta0_pelagic 0 0 1 0 0 0 0 0 1 0 0 0
beta0_yellow 1 1 1 1 0 0 1 0 0 1 0 0
beta1_pelagic 0 0 1 0 0 0 0 1 1 0 0 0
beta1_pH 0 1 0 1 0 0 0 0 1 1 0 0
beta1_yellow 1 1 1 1 0 0 1 0 0 1 0 1
beta2_pelagic 0 0 0 0 0 0 0 0 1 0 0 0
beta2_pH 0 0 0 0 0 0 0 0 0 0 0 1
beta2_yellow 0 1 1 1 1 1 0 0 0 1 1 0
beta3_yellow 0 1 1 1 0 0 1 0 0 1 0 1
beta4_pelagic 0 0 0 0 0 0 0 0 0 1 0 0
mu_beta0_yellow 0 0 0 0 1 0 0 1 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 1 0 0 1 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.126 0.074 -0.260 -0.129 0.025
mu_bc_H[2] -0.096 0.045 -0.174 -0.100 0.003
mu_bc_H[3] -0.434 0.069 -0.566 -0.435 -0.297
mu_bc_H[4] -0.984 0.190 -1.374 -0.982 -0.622
mu_bc_H[5] 0.905 0.940 -0.163 0.708 3.241
mu_bc_H[6] -2.165 0.315 -2.778 -2.166 -1.566
mu_bc_H[7] -0.448 0.107 -0.663 -0.446 -0.243
mu_bc_H[8] 0.245 0.375 -0.352 0.211 1.017
mu_bc_H[9] -0.284 0.137 -0.553 -0.287 0.000
mu_bc_H[10] -0.100 0.071 -0.231 -0.104 0.046
mu_bc_H[11] -0.123 0.037 -0.195 -0.124 -0.050
mu_bc_H[12] -0.251 0.108 -0.481 -0.246 -0.054
mu_bc_H[13] -0.136 0.078 -0.283 -0.137 0.023
mu_bc_H[14] -0.300 0.097 -0.499 -0.297 -0.115
mu_bc_H[15] -0.343 0.051 -0.441 -0.343 -0.243
mu_bc_H[16] -0.256 0.373 -0.910 -0.286 0.557
mu_bc_R[1] 1.357 0.146 1.068 1.357 1.650
mu_bc_R[2] 1.454 0.092 1.276 1.455 1.632
mu_bc_R[3] 1.395 0.140 1.116 1.395 1.660
mu_bc_R[4] 0.906 0.198 0.491 0.918 1.265
mu_bc_R[5] 1.209 0.448 0.304 1.209 2.055
mu_bc_R[6] -1.592 0.397 -2.370 -1.597 -0.801
mu_bc_R[7] 0.250 0.178 -0.097 0.250 0.601
mu_bc_R[8] 0.534 0.190 0.162 0.540 0.911
mu_bc_R[9] 0.295 0.214 -0.158 0.309 0.677
mu_bc_R[10] 1.241 0.165 0.910 1.245 1.559
mu_bc_R[11] 1.037 0.100 0.843 1.037 1.236
mu_bc_R[12] 0.824 0.212 0.394 0.830 1.232
mu_bc_R[13] 1.025 0.104 0.810 1.027 1.228
mu_bc_R[14] 0.901 0.143 0.613 0.901 1.181
mu_bc_R[15] 0.781 0.113 0.556 0.781 0.998
mu_bc_R[16] 1.087 0.127 0.836 1.092 1.327
tau_pH[1] 5.191 0.447 4.364 5.171 6.101
tau_pH[2] 2.049 0.232 1.632 2.038 2.541
tau_pH[3] 2.242 0.218 1.851 2.239 2.699
beta0_pH[1,1] 0.548 0.175 0.211 0.549 0.888
beta0_pH[2,1] 1.368 0.180 1.002 1.376 1.700
beta0_pH[3,1] 1.439 0.186 1.032 1.448 1.777
beta0_pH[4,1] 1.572 0.216 1.102 1.591 1.948
beta0_pH[5,1] -0.874 0.288 -1.484 -0.851 -0.366
beta0_pH[6,1] -0.686 0.458 -1.733 -0.612 -0.015
beta0_pH[7,1] -0.510 0.483 -1.660 -0.465 0.382
beta0_pH[8,1] -0.677 0.290 -1.367 -0.644 -0.214
beta0_pH[9,1] -0.677 0.332 -1.430 -0.641 -0.178
beta0_pH[10,1] 0.361 0.196 -0.059 0.374 0.717
beta0_pH[11,1] -0.096 0.180 -0.457 -0.091 0.242
beta0_pH[12,1] 0.494 0.187 0.113 0.497 0.854
beta0_pH[13,1] -0.006 0.147 -0.297 -0.002 0.276
beta0_pH[14,1] -0.320 0.169 -0.667 -0.317 -0.008
beta0_pH[15,1] -0.041 0.188 -0.423 -0.037 0.316
beta0_pH[16,1] -0.508 0.367 -1.391 -0.453 0.034
beta0_pH[1,2] 2.792 0.170 2.457 2.794 3.115
beta0_pH[2,2] 2.868 0.137 2.605 2.870 3.133
beta0_pH[3,2] 3.036 0.278 2.254 3.093 3.426
beta0_pH[4,2] 2.929 0.145 2.642 2.931 3.199
beta0_pH[5,2] 4.743 1.377 2.939 4.445 8.225
beta0_pH[6,2] 3.120 0.201 2.720 3.120 3.519
beta0_pH[7,2] 1.973 0.172 1.636 1.976 2.300
beta0_pH[8,2] 2.872 0.173 2.540 2.873 3.212
beta0_pH[9,2] 3.433 0.223 3.009 3.438 3.876
beta0_pH[10,2] 3.731 0.202 3.337 3.735 4.120
beta0_pH[11,2] -4.841 0.307 -5.481 -4.836 -4.246
beta0_pH[12,2] -4.796 0.401 -5.599 -4.792 -4.004
beta0_pH[13,2] -4.577 0.405 -5.373 -4.589 -3.796
beta0_pH[14,2] -5.604 0.474 -6.588 -5.596 -4.750
beta0_pH[15,2] -4.274 0.345 -4.914 -4.287 -3.583
beta0_pH[16,2] -4.850 0.391 -5.649 -4.840 -4.087
beta0_pH[1,3] 0.869 0.467 -0.289 0.971 1.522
beta0_pH[2,3] 2.198 0.159 1.885 2.200 2.516
beta0_pH[3,3] 2.516 0.145 2.232 2.515 2.796
beta0_pH[4,3] 2.966 0.160 2.661 2.966 3.292
beta0_pH[5,3] 1.604 1.771 -0.897 1.263 5.866
beta0_pH[6,3] -0.562 0.984 -2.231 -0.754 1.527
beta0_pH[7,3] -2.057 0.546 -3.241 -2.012 -1.142
beta0_pH[8,3] 0.288 0.195 -0.099 0.291 0.663
beta0_pH[9,3] -0.713 0.547 -2.270 -0.589 -0.025
beta0_pH[10,3] 0.375 0.770 -1.753 0.587 1.251
beta0_pH[11,3] -0.158 0.320 -0.754 -0.169 0.510
beta0_pH[12,3] -0.845 0.345 -1.587 -0.822 -0.232
beta0_pH[13,3] -0.150 0.319 -0.769 -0.154 0.481
beta0_pH[14,3] -0.277 0.261 -0.785 -0.280 0.240
beta0_pH[15,3] -0.677 0.286 -1.286 -0.652 -0.180
beta0_pH[16,3] -0.391 0.284 -0.963 -0.388 0.169
beta1_pH[1,1] 3.048 0.322 2.478 3.029 3.739
beta1_pH[2,1] 2.153 0.313 1.660 2.123 2.719
beta1_pH[3,1] 1.962 0.299 1.440 1.941 2.623
beta1_pH[4,1] 2.378 0.361 1.813 2.333 3.208
beta1_pH[5,1] 2.300 0.358 1.728 2.264 3.128
beta1_pH[6,1] 3.902 1.133 2.326 3.659 6.546
beta1_pH[7,1] 2.735 0.944 1.064 2.651 4.964
beta1_pH[8,1] 4.098 1.058 2.645 3.850 6.655
beta1_pH[9,1] 2.366 0.475 1.703 2.297 3.434
beta1_pH[10,1] 2.168 0.266 1.688 2.155 2.734
beta1_pH[11,1] 3.274 0.224 2.855 3.266 3.739
beta1_pH[12,1] 2.543 0.216 2.128 2.540 2.967
beta1_pH[13,1] 2.983 0.216 2.564 2.980 3.404
beta1_pH[14,1] 3.429 0.221 3.008 3.424 3.889
beta1_pH[15,1] 2.543 0.239 2.093 2.537 3.029
beta1_pH[16,1] 4.181 0.640 3.184 4.080 5.644
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.176 0.408 0.000 0.000 1.370
beta1_pH[4,2] 0.025 0.245 0.000 0.000 0.197
beta1_pH[5,2] 0.003 0.102 0.000 0.000 0.005
beta1_pH[6,2] 0.010 0.134 0.000 0.000 0.008
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.003 0.037 0.000 0.000 0.007
beta1_pH[9,2] 0.005 0.085 0.000 0.000 0.007
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.694 0.335 6.069 6.685 7.380
beta1_pH[12,2] 6.467 0.469 5.583 6.442 7.411
beta1_pH[13,2] 6.958 0.446 6.074 6.962 7.828
beta1_pH[14,2] 7.247 0.495 6.338 7.231 8.296
beta1_pH[15,2] 6.755 0.370 6.001 6.760 7.472
beta1_pH[16,2] 7.443 0.424 6.622 7.446 8.303
beta1_pH[1,3] 2.396 0.934 1.266 2.168 4.844
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.130 3.034 0.806 2.822 6.309
beta1_pH[6,3] 2.524 1.485 0.852 2.454 4.148
beta1_pH[7,3] 2.902 0.553 1.973 2.847 4.106
beta1_pH[8,3] 2.751 0.335 2.115 2.743 3.401
beta1_pH[9,3] 2.773 0.558 2.006 2.675 4.274
beta1_pH[10,3] 2.992 0.839 2.016 2.763 5.340
beta1_pH[11,3] 2.744 0.377 2.007 2.740 3.521
beta1_pH[12,3] 4.102 0.434 3.316 4.082 4.993
beta1_pH[13,3] 1.730 0.340 1.047 1.735 2.388
beta1_pH[14,3] 2.531 0.334 1.898 2.528 3.192
beta1_pH[15,3] 1.958 0.314 1.395 1.940 2.604
beta1_pH[16,3] 1.802 0.319 1.192 1.794 2.418
beta2_pH[1,1] 0.486 0.123 0.297 0.470 0.774
beta2_pH[2,1] 0.585 0.323 0.254 0.523 1.306
beta2_pH[3,1] 0.668 0.429 0.243 0.575 1.742
beta2_pH[4,1] 0.491 0.228 0.213 0.455 1.004
beta2_pH[5,1] 1.432 0.969 0.238 1.290 3.703
beta2_pH[6,1] 0.181 0.069 0.087 0.171 0.330
beta2_pH[7,1] 0.008 0.041 0.000 0.000 0.049
beta2_pH[8,1] 0.238 0.088 0.120 0.223 0.451
beta2_pH[9,1] 0.428 0.253 0.159 0.389 0.900
beta2_pH[10,1] 0.639 0.310 0.300 0.580 1.322
beta2_pH[11,1] 0.782 0.210 0.473 0.745 1.269
beta2_pH[12,1] 1.345 0.455 0.733 1.250 2.415
beta2_pH[13,1] 0.733 0.229 0.404 0.696 1.247
beta2_pH[14,1] 0.828 0.201 0.525 0.798 1.292
beta2_pH[15,1] 0.790 0.287 0.410 0.735 1.488
beta2_pH[16,1] 0.358 0.161 0.171 0.315 0.793
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -1.619 10.292 -21.578 -2.144 19.272
beta2_pH[4,2] -1.457 10.444 -21.403 -1.734 19.328
beta2_pH[5,2] -0.451 10.581 -21.094 -0.672 20.512
beta2_pH[6,2] -0.366 10.432 -20.828 -0.694 20.197
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] -0.499 10.561 -21.237 -0.529 20.376
beta2_pH[9,2] -0.307 10.465 -20.800 -0.627 20.643
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -8.981 3.912 -18.524 -8.061 -3.947
beta2_pH[12,2] -6.975 4.647 -18.144 -6.084 -0.897
beta2_pH[13,2] -6.928 4.500 -18.217 -5.931 -1.565
beta2_pH[14,2] -7.715 4.183 -17.865 -6.716 -2.413
beta2_pH[15,2] -8.856 4.022 -18.638 -8.000 -3.701
beta2_pH[16,2] -9.130 3.894 -18.730 -8.293 -3.901
beta2_pH[1,3] 4.510 5.321 0.156 2.448 18.286
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.628 6.308 0.325 7.429 23.579
beta2_pH[6,3] 8.780 6.451 0.208 7.543 24.120
beta2_pH[7,3] 8.374 6.319 0.656 7.105 23.452
beta2_pH[8,3] 9.606 5.848 1.455 8.539 23.586
beta2_pH[9,3] 8.375 6.596 0.369 7.293 24.053
beta2_pH[10,3] 7.767 6.657 0.350 6.661 23.594
beta2_pH[11,3] -2.233 1.835 -7.191 -1.684 -0.638
beta2_pH[12,3] -2.421 1.800 -7.551 -1.904 -0.938
beta2_pH[13,3] -2.801 2.190 -8.925 -2.109 -0.752
beta2_pH[14,3] -2.822 2.135 -9.126 -2.158 -0.875
beta2_pH[15,3] -2.980 2.246 -9.345 -2.265 -0.966
beta2_pH[16,3] -3.022 2.282 -9.758 -2.300 -0.882
beta3_pH[1,1] 35.818 0.804 34.301 35.792 37.475
beta3_pH[2,1] 33.584 1.174 31.585 33.470 36.093
beta3_pH[3,1] 33.711 1.028 31.805 33.661 35.846
beta3_pH[4,1] 33.788 1.197 31.631 33.745 36.315
beta3_pH[5,1] 27.725 1.115 26.494 27.467 30.916
beta3_pH[6,1] 38.758 3.088 33.034 38.608 45.090
beta3_pH[7,1] 30.602 8.011 18.426 30.119 45.118
beta3_pH[8,1] 40.134 2.194 36.164 39.887 44.985
beta3_pH[9,1] 30.575 1.466 27.852 30.523 33.631
beta3_pH[10,1] 32.841 0.941 31.057 32.822 34.802
beta3_pH[11,1] 30.307 0.477 29.392 30.301 31.236
beta3_pH[12,1] 30.167 0.400 29.349 30.176 30.956
beta3_pH[13,1] 33.170 0.600 32.043 33.161 34.346
beta3_pH[14,1] 32.030 0.450 31.169 32.023 32.919
beta3_pH[15,1] 31.166 0.655 29.864 31.162 32.441
beta3_pH[16,1] 32.097 1.080 30.244 31.973 34.444
beta3_pH[1,2] 30.019 7.886 18.441 29.072 44.833
beta3_pH[2,2] 30.204 8.069 18.577 29.170 44.912
beta3_pH[3,2] 31.534 8.518 18.487 30.971 44.549
beta3_pH[4,2] 29.906 8.013 18.379 28.719 44.839
beta3_pH[5,2] 29.948 7.955 18.506 29.067 44.867
beta3_pH[6,2] 30.103 8.029 18.395 29.150 45.069
beta3_pH[7,2] 29.925 7.898 18.487 28.926 44.844
beta3_pH[8,2] 29.878 8.020 18.383 28.702 44.762
beta3_pH[9,2] 30.285 7.936 18.526 29.501 44.830
beta3_pH[10,2] 29.833 7.924 18.462 28.723 44.954
beta3_pH[11,2] 43.403 0.177 43.124 43.384 43.771
beta3_pH[12,2] 43.190 0.196 42.873 43.152 43.664
beta3_pH[13,2] 43.858 0.151 43.472 43.897 44.059
beta3_pH[14,2] 43.308 0.198 43.052 43.261 43.801
beta3_pH[15,2] 43.409 0.187 43.115 43.388 43.808
beta3_pH[16,2] 43.495 0.185 43.161 43.493 43.837
beta3_pH[1,3] 39.162 2.016 34.382 39.774 42.356
beta3_pH[2,3] 30.165 8.050 18.358 29.451 45.015
beta3_pH[3,3] 30.147 7.968 18.547 29.135 45.104
beta3_pH[4,3] 30.194 7.967 18.548 29.314 44.923
beta3_pH[5,3] 26.671 6.667 18.289 25.197 42.477
beta3_pH[6,3] 27.867 6.351 18.850 25.849 44.140
beta3_pH[7,3] 26.569 0.935 24.996 26.448 28.797
beta3_pH[8,3] 41.493 0.265 41.039 41.486 41.944
beta3_pH[9,3] 33.039 1.493 27.992 33.457 34.228
beta3_pH[10,3] 35.588 1.212 32.252 36.022 36.873
beta3_pH[11,3] 41.790 0.823 40.195 41.817 43.293
beta3_pH[12,3] 41.715 0.379 40.944 41.740 42.456
beta3_pH[13,3] 42.789 0.904 41.086 42.784 44.886
beta3_pH[14,3] 41.100 0.559 39.937 41.119 42.105
beta3_pH[15,3] 42.605 0.678 41.209 42.672 43.771
beta3_pH[16,3] 42.921 0.697 41.314 43.018 44.068
beta0_pelagic[1] 2.202 0.127 1.955 2.201 2.460
beta0_pelagic[2] 1.519 0.122 1.282 1.519 1.755
beta0_pelagic[3] 0.141 0.410 -1.029 0.228 0.695
beta0_pelagic[4] 0.116 0.579 -1.644 0.225 0.906
beta0_pelagic[5] 1.185 0.248 0.683 1.194 1.658
beta0_pelagic[6] 1.470 0.269 0.883 1.487 1.971
beta0_pelagic[7] 1.638 0.213 1.256 1.625 2.112
beta0_pelagic[8] 1.762 0.197 1.377 1.756 2.178
beta0_pelagic[9] 2.491 0.316 1.865 2.497 3.071
beta0_pelagic[10] 2.499 0.212 2.029 2.514 2.883
beta0_pelagic[11] -0.140 0.594 -1.507 -0.059 0.662
beta0_pelagic[12] 1.691 0.143 1.408 1.696 1.968
beta0_pelagic[13] 0.308 0.215 -0.152 0.323 0.669
beta0_pelagic[14] -0.147 0.286 -0.788 -0.129 0.340
beta0_pelagic[15] -0.268 0.135 -0.534 -0.272 0.007
beta0_pelagic[16] 0.238 0.344 -0.591 0.332 0.669
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 0.976 0.538 0.328 0.834 2.585
beta1_pelagic[4] 1.090 0.608 0.193 0.974 2.915
beta1_pelagic[5] -0.083 0.314 -0.711 -0.083 0.517
beta1_pelagic[6] -0.100 0.462 -0.880 -0.155 0.761
beta1_pelagic[7] -0.021 0.309 -0.621 -0.020 0.593
beta1_pelagic[8] -0.008 0.277 -0.547 -0.012 0.551
beta1_pelagic[9] 0.213 0.480 -0.758 0.326 0.951
beta1_pelagic[10] 0.060 0.276 -0.467 0.058 0.606
beta1_pelagic[11] 4.218 1.451 2.171 4.073 7.140
beta1_pelagic[12] 2.778 0.301 2.208 2.767 3.370
beta1_pelagic[13] 2.904 0.773 1.723 2.795 4.683
beta1_pelagic[14] 4.693 1.106 2.905 4.595 6.996
beta1_pelagic[15] 2.919 0.251 2.420 2.918 3.418
beta1_pelagic[16] 3.845 1.265 2.712 3.327 7.343
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 2.200 2.188 0.089 1.516 7.691
beta2_pelagic[4] 2.244 2.280 0.159 1.590 8.431
beta2_pelagic[5] -0.034 0.672 -1.451 -0.023 1.338
beta2_pelagic[6] -0.088 0.711 -1.491 -0.152 1.406
beta2_pelagic[7] 0.011 0.687 -1.408 0.007 1.444
beta2_pelagic[8] -0.001 0.651 -1.353 0.004 1.396
beta2_pelagic[9] 0.204 0.675 -1.222 0.271 1.517
beta2_pelagic[10] 0.033 0.624 -1.264 0.037 1.352
beta2_pelagic[11] 1.367 3.181 0.087 0.208 11.161
beta2_pelagic[12] 6.176 4.708 1.256 4.841 19.625
beta2_pelagic[13] 0.919 1.817 0.190 0.467 4.851
beta2_pelagic[14] 0.290 0.129 0.148 0.264 0.582
beta2_pelagic[15] 6.347 4.863 1.428 5.033 19.211
beta2_pelagic[16] 4.526 5.312 0.168 3.001 19.065
beta3_pelagic[1] 29.763 7.893 18.499 28.880 44.721
beta3_pelagic[2] 29.935 7.988 18.505 28.958 45.032
beta3_pelagic[3] 29.810 4.612 21.971 29.762 42.082
beta3_pelagic[4] 25.429 3.304 19.952 25.351 34.589
beta3_pelagic[5] 30.315 8.238 18.594 28.823 45.319
beta3_pelagic[6] 31.883 6.759 18.911 31.952 44.237
beta3_pelagic[7] 29.649 7.587 18.513 28.663 44.734
beta3_pelagic[8] 29.465 7.894 18.501 27.993 44.839
beta3_pelagic[9] 30.899 6.106 19.350 30.871 43.156
beta3_pelagic[10] 29.275 8.012 18.365 27.710 44.778
beta3_pelagic[11] 42.560 1.767 38.463 42.908 45.632
beta3_pelagic[12] 43.466 0.258 43.012 43.455 43.952
beta3_pelagic[13] 42.784 1.311 40.275 42.766 45.486
beta3_pelagic[14] 42.778 1.697 39.325 42.804 45.718
beta3_pelagic[15] 43.181 0.259 42.577 43.187 43.692
beta3_pelagic[16] 43.272 0.886 41.230 43.251 45.525
mu_beta0_pelagic[1] 0.918 0.881 -1.077 0.962 2.591
mu_beta0_pelagic[2] 1.820 0.384 1.063 1.818 2.578
mu_beta0_pelagic[3] 0.279 0.511 -0.801 0.287 1.284
tau_beta0_pelagic[1] 0.729 0.774 0.059 0.480 2.870
tau_beta0_pelagic[2] 2.870 3.502 0.294 2.005 10.343
tau_beta0_pelagic[3] 1.408 1.127 0.156 1.105 4.495
beta0_yellow[1] -0.535 0.189 -0.939 -0.518 -0.229
beta0_yellow[2] 0.497 0.175 0.156 0.508 0.799
beta0_yellow[3] -0.302 0.189 -0.677 -0.298 0.053
beta0_yellow[4] 0.785 0.377 -0.349 0.870 1.198
beta0_yellow[5] -0.951 0.550 -1.996 -0.950 0.037
beta0_yellow[6] 0.566 0.446 -0.103 0.426 1.363
beta0_yellow[7] 1.027 0.221 0.695 1.041 1.350
beta0_yellow[8] 0.792 0.552 -0.902 0.955 1.298
beta0_yellow[9] -0.048 0.373 -0.636 -0.067 0.724
beta0_yellow[10] 0.239 0.156 -0.067 0.240 0.543
beta0_yellow[11] -1.432 0.923 -2.793 -1.736 0.076
beta0_yellow[12] -3.722 0.439 -4.642 -3.704 -2.924
beta0_yellow[13] -3.814 0.485 -4.844 -3.783 -2.948
beta0_yellow[14] -2.009 0.704 -3.123 -2.110 -0.167
beta0_yellow[15] -2.922 0.436 -3.810 -2.886 -2.153
beta0_yellow[16] -2.370 0.477 -3.282 -2.389 -1.391
beta1_yellow[1] 0.578 0.797 0.000 0.399 2.190
beta1_yellow[2] 1.070 0.408 0.585 1.021 1.888
beta1_yellow[3] 0.661 0.275 0.032 0.666 1.212
beta1_yellow[4] 1.530 0.984 0.642 1.225 4.721
beta1_yellow[5] 2.157 3.083 0.000 2.311 5.607
beta1_yellow[6] 1.517 1.110 0.000 2.035 2.894
beta1_yellow[7] 8.537 11.410 1.585 5.891 29.554
beta1_yellow[8] 1.657 3.826 0.000 0.966 6.816
beta1_yellow[9] 1.440 0.615 0.000 1.488 2.531
beta1_yellow[10] 2.415 0.495 1.556 2.381 3.417
beta1_yellow[11] 2.079 0.712 0.694 2.102 3.352
beta1_yellow[12] 2.526 0.451 1.721 2.506 3.475
beta1_yellow[13] 2.936 0.482 2.101 2.906 3.967
beta1_yellow[14] 2.198 0.736 0.694 2.202 3.396
beta1_yellow[15] 2.161 0.431 1.380 2.127 3.053
beta1_yellow[16] 2.125 0.478 1.106 2.140 3.050
beta2_yellow[1] -2.619 2.879 -9.549 -2.049 2.263
beta2_yellow[2] -2.662 2.262 -9.263 -2.032 -0.184
beta2_yellow[3] -2.856 2.467 -9.379 -2.219 -0.149
beta2_yellow[4] -2.371 2.483 -8.975 -1.647 -0.072
beta2_yellow[5] -3.473 3.572 -10.806 -3.310 4.275
beta2_yellow[6] 1.814 4.115 -8.044 2.324 9.213
beta2_yellow[7] -4.854 3.027 -11.711 -4.471 -0.829
beta2_yellow[8] -2.048 4.039 -9.786 -1.982 6.810
beta2_yellow[9] 3.196 3.232 -4.888 3.092 9.629
beta2_yellow[10] -4.761 2.424 -10.291 -4.579 -0.894
beta2_yellow[11] -3.255 2.122 -8.438 -2.952 -0.125
beta2_yellow[12] -3.900 2.039 -9.222 -3.482 -1.282
beta2_yellow[13] -3.648 1.696 -8.089 -3.328 -1.416
beta2_yellow[14] -3.642 2.157 -9.286 -3.281 -0.140
beta2_yellow[15] -3.494 1.977 -8.824 -3.025 -1.027
beta2_yellow[16] -3.886 1.769 -8.037 -3.576 -1.422
beta3_yellow[1] 27.071 7.659 18.328 23.979 44.426
beta3_yellow[2] 29.223 1.838 25.985 29.013 32.793
beta3_yellow[3] 32.917 3.225 24.751 32.936 39.675
beta3_yellow[4] 28.753 3.698 20.234 27.922 36.073
beta3_yellow[5] 32.133 4.998 19.377 33.146 42.873
beta3_yellow[6] 36.339 6.571 19.243 39.444 42.581
beta3_yellow[7] 20.039 1.707 18.368 19.926 21.475
beta3_yellow[8] 26.406 6.674 18.320 24.808 44.008
beta3_yellow[9] 37.134 3.512 24.288 37.562 42.881
beta3_yellow[10] 29.342 0.578 27.984 29.409 30.086
beta3_yellow[11] 40.178 7.365 28.118 45.046 45.960
beta3_yellow[12] 43.321 0.396 42.530 43.304 44.126
beta3_yellow[13] 44.858 0.373 44.041 44.909 45.477
beta3_yellow[14] 43.350 3.390 30.817 44.222 45.855
beta3_yellow[15] 45.225 0.508 44.200 45.251 45.968
beta3_yellow[16] 44.611 0.627 43.479 44.592 45.817
mu_beta0_yellow[1] 0.098 0.552 -1.049 0.100 1.200
mu_beta0_yellow[2] 0.261 0.472 -0.731 0.279 1.115
mu_beta0_yellow[3] -2.287 0.762 -3.484 -2.412 -0.456
tau_beta0_yellow[1] 1.907 2.573 0.095 1.219 7.179
tau_beta0_yellow[2] 1.607 1.551 0.160 1.154 5.678
tau_beta0_yellow[3] 1.120 1.748 0.072 0.597 5.250
beta0_black[1] -0.091 0.156 -0.390 -0.092 0.220
beta0_black[2] 1.914 0.125 1.672 1.914 2.153
beta0_black[3] 1.318 0.131 1.059 1.315 1.578
beta0_black[4] 2.427 0.130 2.179 2.424 2.681
beta0_black[5] 1.492 1.956 -3.269 1.630 5.217
beta0_black[6] 1.553 1.875 -2.859 1.639 5.380
beta0_black[7] 1.573 1.982 -2.850 1.639 5.678
beta0_black[8] 1.284 0.220 0.860 1.280 1.723
beta0_black[9] 2.443 0.246 1.935 2.457 2.912
beta0_black[10] 1.469 0.135 1.206 1.471 1.731
beta0_black[11] 3.487 0.148 3.203 3.488 3.775
beta0_black[12] 4.856 0.169 4.528 4.856 5.184
beta0_black[13] -0.148 0.256 -0.656 -0.139 0.305
beta0_black[14] 2.852 0.155 2.547 2.853 3.147
beta0_black[15] 1.290 0.153 0.999 1.289 1.602
beta0_black[16] 4.269 0.157 3.963 4.267 4.576
beta2_black[1] 3.545 2.299 0.789 2.972 9.504
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.941 1.642 -6.543 -1.392 -0.355
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.757 1.001 39.957 41.899 43.068
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.210 0.848 37.350 39.305 40.566
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.253 0.190 -0.627 -0.255 0.121
beta4_black[2] 0.246 0.179 -0.094 0.243 0.606
beta4_black[3] -0.934 0.188 -1.304 -0.937 -0.562
beta4_black[4] 0.413 0.209 0.002 0.418 0.818
beta4_black[5] 0.189 2.571 -4.700 0.095 5.000
beta4_black[6] 0.202 2.503 -4.343 0.105 5.150
beta4_black[7] 0.177 2.376 -4.442 0.086 4.939
beta4_black[8] -0.691 0.373 -1.426 -0.684 0.016
beta4_black[9] 1.475 1.042 -0.152 1.330 3.815
beta4_black[10] 0.029 0.187 -0.325 0.026 0.389
beta4_black[11] -0.698 0.207 -1.111 -0.695 -0.281
beta4_black[12] 0.166 0.318 -0.410 0.159 0.805
beta4_black[13] -1.183 0.221 -1.631 -1.178 -0.753
beta4_black[14] -0.187 0.230 -0.634 -0.192 0.260
beta4_black[15] -0.893 0.208 -1.320 -0.887 -0.497
beta4_black[16] -0.598 0.224 -1.032 -0.603 -0.156
mu_beta0_black[1] 1.258 0.909 -0.796 1.302 3.000
mu_beta0_black[2] 1.552 0.919 -0.645 1.628 3.238
mu_beta0_black[3] 2.513 0.993 0.366 2.527 4.457
tau_beta0_black[1] 0.620 0.582 0.056 0.441 2.139
tau_beta0_black[2] 1.895 3.482 0.056 0.829 10.561
tau_beta0_black[3] 0.239 0.163 0.048 0.200 0.644
beta0_dsr[11] -2.920 0.283 -3.471 -2.926 -2.379
beta0_dsr[12] 4.523 0.292 3.979 4.523 5.072
beta0_dsr[13] -1.340 0.317 -1.942 -1.327 -0.772
beta0_dsr[14] -3.712 0.507 -4.688 -3.703 -2.729
beta0_dsr[15] -1.947 0.276 -2.480 -1.950 -1.395
beta0_dsr[16] -3.002 0.359 -3.733 -3.001 -2.300
beta1_dsr[11] 4.851 0.299 4.260 4.854 5.436
beta1_dsr[12] 7.080 10.564 2.250 5.168 21.521
beta1_dsr[13] 2.858 0.355 2.257 2.842 3.474
beta1_dsr[14] 6.374 0.530 5.363 6.372 7.381
beta1_dsr[15] 3.341 0.277 2.792 3.345 3.872
beta1_dsr[16] 5.820 0.378 5.092 5.808 6.581
beta2_dsr[11] -8.403 2.414 -13.738 -8.022 -4.634
beta2_dsr[12] -7.124 2.697 -12.932 -6.954 -2.176
beta2_dsr[13] -6.458 2.717 -12.331 -6.438 -1.404
beta2_dsr[14] -6.231 2.668 -11.742 -6.170 -1.857
beta2_dsr[15] -7.797 2.418 -13.490 -7.497 -3.816
beta2_dsr[16] -7.987 2.286 -13.256 -7.705 -4.362
beta3_dsr[11] 43.491 0.150 43.216 43.489 43.784
beta3_dsr[12] 33.977 0.743 32.204 34.130 34.819
beta3_dsr[13] 43.232 0.332 42.731 43.181 43.845
beta3_dsr[14] 43.339 0.225 43.082 43.274 43.935
beta3_dsr[15] 43.510 0.185 43.169 43.510 43.857
beta3_dsr[16] 43.439 0.158 43.166 43.425 43.761
beta4_dsr[11] 0.591 0.215 0.173 0.586 1.013
beta4_dsr[12] 0.250 0.450 -0.627 0.244 1.198
beta4_dsr[13] -0.172 0.216 -0.595 -0.168 0.242
beta4_dsr[14] 0.152 0.249 -0.348 0.150 0.644
beta4_dsr[15] 0.731 0.216 0.321 0.730 1.149
beta4_dsr[16] 0.144 0.221 -0.297 0.147 0.574
beta0_slope[11] -1.939 0.161 -2.255 -1.940 -1.628
beta0_slope[12] -4.667 0.265 -5.194 -4.664 -4.173
beta0_slope[13] -1.336 0.194 -1.734 -1.322 -0.993
beta0_slope[14] -2.641 0.177 -2.994 -2.641 -2.300
beta0_slope[15] -1.368 0.170 -1.697 -1.368 -1.024
beta0_slope[16] -2.720 0.172 -3.060 -2.717 -2.385
beta1_slope[11] 4.597 0.298 4.025 4.594 5.185
beta1_slope[12] 4.999 0.530 4.013 4.991 6.034
beta1_slope[13] 2.904 0.476 2.236 2.852 4.096
beta1_slope[14] 6.525 0.557 5.477 6.510 7.675
beta1_slope[15] 3.053 0.288 2.493 3.054 3.621
beta1_slope[16] 5.382 0.395 4.631 5.373 6.187
beta2_slope[11] 7.967 2.297 4.348 7.665 13.286
beta2_slope[12] 7.154 2.477 2.674 6.939 12.770
beta2_slope[13] 5.764 2.945 0.486 5.871 11.617
beta2_slope[14] 6.524 2.401 2.470 6.343 11.753
beta2_slope[15] 7.517 2.357 3.666 7.197 13.066
beta2_slope[16] 7.602 2.349 3.834 7.276 13.104
beta3_slope[11] 43.477 0.154 43.191 43.474 43.779
beta3_slope[12] 43.414 0.237 43.059 43.384 43.879
beta3_slope[13] 43.622 0.414 42.925 43.690 44.203
beta3_slope[14] 43.317 0.171 43.093 43.277 43.755
beta3_slope[15] 43.512 0.199 43.149 43.506 43.887
beta3_slope[16] 43.456 0.170 43.172 43.444 43.797
beta4_slope[11] -0.578 0.217 -1.024 -0.574 -0.156
beta4_slope[12] -1.379 0.660 -2.903 -1.294 -0.336
beta4_slope[13] 0.049 0.214 -0.360 0.046 0.485
beta4_slope[14] -0.179 0.256 -0.682 -0.188 0.334
beta4_slope[15] -0.726 0.216 -1.165 -0.722 -0.326
beta4_slope[16] -0.203 0.233 -0.656 -0.208 0.249
sigma_H[1] 0.203 0.054 0.106 0.201 0.316
sigma_H[2] 0.171 0.030 0.120 0.169 0.237
sigma_H[3] 0.197 0.043 0.120 0.195 0.287
sigma_H[4] 0.420 0.075 0.298 0.411 0.587
sigma_H[5] 1.010 0.212 0.625 0.998 1.468
sigma_H[6] 0.410 0.204 0.045 0.408 0.838
sigma_H[7] 0.300 0.059 0.208 0.293 0.437
sigma_H[8] 0.410 0.087 0.266 0.403 0.591
sigma_H[9] 0.522 0.126 0.330 0.505 0.798
sigma_H[10] 0.208 0.043 0.135 0.205 0.303
sigma_H[11] 0.278 0.046 0.202 0.275 0.382
sigma_H[12] 0.437 0.167 0.209 0.415 0.780
sigma_H[13] 0.214 0.037 0.151 0.211 0.293
sigma_H[14] 0.509 0.094 0.346 0.504 0.718
sigma_H[15] 0.246 0.040 0.181 0.243 0.335
sigma_H[16] 0.225 0.044 0.153 0.220 0.329
lambda_H[1] 3.047 4.080 0.149 1.688 13.067
lambda_H[2] 8.126 7.607 0.781 5.911 29.172
lambda_H[3] 6.476 10.012 0.265 3.373 31.660
lambda_H[4] 0.006 0.004 0.001 0.005 0.016
lambda_H[5] 4.191 9.839 0.034 1.077 30.591
lambda_H[6] 8.513 16.013 0.008 1.403 58.911
lambda_H[7] 0.013 0.009 0.002 0.011 0.036
lambda_H[8] 8.399 10.542 0.166 4.720 38.927
lambda_H[9] 0.015 0.010 0.003 0.013 0.042
lambda_H[10] 0.277 0.473 0.033 0.183 1.013
lambda_H[11] 0.262 0.442 0.011 0.126 1.197
lambda_H[12] 4.841 6.304 0.204 2.787 20.921
lambda_H[13] 3.432 3.137 0.257 2.568 12.239
lambda_H[14] 3.269 4.482 0.220 1.979 14.193
lambda_H[15] 0.026 0.042 0.004 0.017 0.106
lambda_H[16] 0.821 1.160 0.039 0.421 4.026
mu_lambda_H[1] 4.325 1.879 1.234 4.140 8.236
mu_lambda_H[2] 3.841 1.912 0.639 3.713 7.946
mu_lambda_H[3] 3.468 1.857 0.756 3.184 7.600
sigma_lambda_H[1] 8.608 4.295 2.136 7.902 18.257
sigma_lambda_H[2] 8.372 4.550 1.050 7.849 17.810
sigma_lambda_H[3] 6.189 3.941 0.948 5.411 15.961
beta_H[1,1] 6.907 1.065 4.356 7.062 8.662
beta_H[2,1] 9.878 0.484 8.904 9.886 10.781
beta_H[3,1] 8.028 0.756 6.212 8.120 9.269
beta_H[4,1] 9.405 7.955 -7.140 9.626 24.695
beta_H[5,1] 0.162 2.302 -4.625 0.325 4.025
beta_H[6,1] 3.173 3.932 -7.166 4.676 7.536
beta_H[7,1] 0.370 5.774 -11.391 0.749 11.075
beta_H[8,1] 1.271 3.290 -2.245 1.228 3.376
beta_H[9,1] 13.015 5.680 1.786 13.043 24.297
beta_H[10,1] 6.959 1.754 3.277 7.022 10.287
beta_H[11,1] 5.105 3.553 -3.241 5.868 9.964
beta_H[12,1] 2.608 1.039 0.752 2.552 4.967
beta_H[13,1] 9.060 0.889 7.159 9.119 10.585
beta_H[14,1] 2.181 1.034 0.111 2.171 4.249
beta_H[15,1] -6.102 3.804 -12.721 -6.388 2.406
beta_H[16,1] 3.506 2.701 -0.911 3.137 9.853
beta_H[1,2] 7.897 0.246 7.404 7.905 8.351
beta_H[2,2] 10.024 0.137 9.754 10.023 10.288
beta_H[3,2] 8.951 0.196 8.567 8.953 9.333
beta_H[4,2] 3.622 1.517 0.804 3.589 6.751
beta_H[5,2] 1.966 0.951 0.073 1.992 3.764
beta_H[6,2] 5.757 1.009 3.380 5.928 7.308
beta_H[7,2] 2.676 1.082 0.726 2.600 4.935
beta_H[8,2] 3.031 0.983 1.454 3.126 4.267
beta_H[9,2] 3.478 1.101 1.395 3.475 5.772
beta_H[10,2] 8.199 0.341 7.490 8.199 8.844
beta_H[11,2] 9.771 0.640 8.854 9.652 11.263
beta_H[12,2] 3.938 0.366 3.265 3.926 4.689
beta_H[13,2] 9.121 0.250 8.662 9.107 9.628
beta_H[14,2] 4.017 0.349 3.338 4.011 4.740
beta_H[15,2] 11.371 0.679 9.928 11.411 12.567
beta_H[16,2] 4.502 0.795 3.046 4.500 6.118
beta_H[1,3] 8.463 0.243 8.020 8.453 8.962
beta_H[2,3] 10.069 0.116 9.841 10.071 10.301
beta_H[3,3] 9.616 0.163 9.304 9.612 9.951
beta_H[4,3] -2.557 0.872 -4.290 -2.550 -0.839
beta_H[5,3] 3.822 0.615 2.531 3.852 4.974
beta_H[6,3] 7.940 1.179 6.394 7.571 10.583
beta_H[7,3] -2.787 0.644 -4.133 -2.772 -1.585
beta_H[8,3] 5.230 0.444 4.663 5.181 6.073
beta_H[9,3] -2.872 0.741 -4.356 -2.862 -1.411
beta_H[10,3] 8.692 0.274 8.175 8.691 9.239
beta_H[11,3] 8.542 0.283 7.922 8.573 9.024
beta_H[12,3] 5.256 0.321 4.504 5.294 5.776
beta_H[13,3] 8.842 0.173 8.470 8.843 9.172
beta_H[14,3] 5.713 0.286 5.078 5.735 6.226
beta_H[15,3] 10.361 0.316 9.749 10.352 10.981
beta_H[16,3] 6.224 0.603 4.919 6.282 7.239
beta_H[1,4] 8.260 0.176 7.880 8.270 8.576
beta_H[2,4] 10.130 0.120 9.871 10.139 10.344
beta_H[3,4] 10.124 0.164 9.766 10.136 10.413
beta_H[4,4] 11.817 0.447 10.895 11.841 12.677
beta_H[5,4] 5.497 0.740 4.277 5.429 7.148
beta_H[6,4] 7.082 0.898 5.032 7.368 8.278
beta_H[7,4] 8.214 0.345 7.534 8.216 8.864
beta_H[8,4] 6.709 0.240 6.256 6.712 7.141
beta_H[9,4] 7.190 0.466 6.305 7.187 8.163
beta_H[10,4] 7.713 0.231 7.281 7.702 8.204
beta_H[11,4] 9.382 0.202 8.976 9.383 9.761
beta_H[12,4] 7.136 0.211 6.725 7.136 7.570
beta_H[13,4] 9.049 0.142 8.762 9.051 9.328
beta_H[14,4] 7.733 0.224 7.302 7.731 8.191
beta_H[15,4] 9.471 0.232 9.006 9.471 9.931
beta_H[16,4] 9.353 0.239 8.913 9.345 9.847
beta_H[1,5] 8.979 0.148 8.678 8.982 9.258
beta_H[2,5] 10.784 0.095 10.603 10.780 10.979
beta_H[3,5] 10.914 0.170 10.617 10.907 11.273
beta_H[4,5] 8.378 0.454 7.517 8.360 9.320
beta_H[5,5] 5.453 0.589 4.109 5.495 6.491
beta_H[6,5] 8.797 0.619 7.900 8.646 10.283
beta_H[7,5] 6.782 0.330 6.173 6.779 7.453
beta_H[8,5] 8.216 0.197 7.857 8.207 8.624
beta_H[9,5] 8.200 0.471 7.266 8.194 9.156
beta_H[10,5] 10.100 0.227 9.645 10.097 10.545
beta_H[11,5] 11.513 0.229 11.054 11.511 11.971
beta_H[12,5] 8.481 0.195 8.103 8.482 8.876
beta_H[13,5] 10.015 0.133 9.766 10.015 10.288
beta_H[14,5] 9.205 0.234 8.770 9.194 9.707
beta_H[15,5] 11.166 0.240 10.692 11.165 11.633
beta_H[16,5] 9.918 0.179 9.553 9.924 10.248
beta_H[1,6] 10.187 0.188 9.850 10.173 10.607
beta_H[2,6] 11.510 0.109 11.293 11.511 11.713
beta_H[3,6] 10.817 0.161 10.472 10.828 11.098
beta_H[4,6] 12.905 0.807 11.247 12.934 14.409
beta_H[5,6] 5.920 0.599 4.784 5.913 7.134
beta_H[6,6] 8.833 0.656 7.132 8.937 9.785
beta_H[7,6] 9.820 0.551 8.699 9.822 10.885
beta_H[8,6] 9.525 0.261 9.039 9.537 9.960
beta_H[9,6] 8.476 0.789 6.927 8.470 10.042
beta_H[10,6] 9.502 0.317 8.824 9.527 10.070
beta_H[11,6] 10.810 0.353 10.044 10.830 11.443
beta_H[12,6] 9.374 0.254 8.885 9.366 9.906
beta_H[13,6] 11.047 0.157 10.750 11.040 11.385
beta_H[14,6] 9.815 0.297 9.214 9.817 10.402
beta_H[15,6] 10.836 0.425 9.987 10.847 11.649
beta_H[16,6] 10.533 0.239 10.020 10.538 10.979
beta_H[1,7] 10.876 0.878 8.668 10.986 12.302
beta_H[2,7] 12.212 0.427 11.292 12.223 13.019
beta_H[3,7] 10.560 0.661 9.138 10.631 11.646
beta_H[4,7] 2.419 4.086 -5.009 2.252 10.967
beta_H[5,7] 6.449 1.804 2.943 6.406 10.527
beta_H[6,7] 9.646 2.420 4.881 9.618 15.461
beta_H[7,7] 10.631 2.743 5.304 10.571 16.184
beta_H[8,7] 10.919 0.911 9.353 10.892 12.466
beta_H[9,7] 4.320 4.097 -4.103 4.297 12.197
beta_H[10,7] 9.885 1.445 7.186 9.814 12.926
beta_H[11,7] 11.004 1.717 7.805 10.929 14.666
beta_H[12,7] 10.002 0.920 7.955 10.063 11.603
beta_H[13,7] 11.656 0.725 9.954 11.730 12.811
beta_H[14,7] 10.388 0.959 8.372 10.426 12.067
beta_H[15,7] 11.995 2.206 7.695 12.011 16.320
beta_H[16,7] 12.331 1.283 10.135 12.177 15.308
beta0_H[1] 8.408 13.697 -18.022 8.567 35.250
beta0_H[2] 10.561 6.403 -2.012 10.521 23.485
beta0_H[3] 9.537 9.347 -9.827 9.820 28.847
beta0_H[4] 0.630 183.296 -382.000 4.581 372.283
beta0_H[5] 3.876 25.184 -42.851 4.448 47.719
beta0_H[6] 6.609 51.452 -109.063 7.537 113.122
beta0_H[7] 5.759 134.820 -254.429 5.454 281.001
beta0_H[8] 6.330 29.571 -12.291 6.449 27.317
beta0_H[9] 4.536 123.532 -246.580 7.546 251.885
beta0_H[10] 8.546 34.994 -62.420 9.126 77.663
beta0_H[11] 9.256 48.843 -91.795 9.747 109.708
beta0_H[12] 6.697 11.665 -17.699 6.803 30.582
beta0_H[13] 9.980 10.703 -10.170 9.949 32.729
beta0_H[14] 7.073 12.326 -17.590 7.059 32.357
beta0_H[15] 9.456 106.019 -209.042 11.071 233.453
beta0_H[16] 7.898 25.422 -42.739 7.625 58.998